Soft Threshold De-noising Method Research Articles

CEEMDAN-LWT De-Noising Method for Pipe-Jacking Inertial Guidance System Based on Fiber Optic Gyroscope.

An inertial guidance system based on a fiber optic gyroscope (FOG) is an effective way to guide long-distance curved pipe jacking. However, environmental disturbances such as vibration, electromagnetism, and temperature will cause the FOG signal to generate significant random noise. The random noise will overwhelm the effective signal. Therefore, it is necessary to eliminate the random noise. This study proposes a hybrid de-noising method, namely complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-lifting wavelet transform (LWT). Firstly, the FOG signal is extracted using a sliding window and decomposed by CEEMDAN to obtain the intrinsic modal function (IMF) with N different scales and one residual. Subsequently, the effective IMF components are selected according to the correlation coefficient between the IMF components and the FOG signal. Due to the low resolution of the CEEMDAN method for high-frequency components, the selected high-frequency IMF components are decomposed with lifting wavelet transform to increase the resolution of the signal. The detailed signals of the LWT decomposition are de-noised using the soft threshold de-noising method, and then the signal is reconstructed. Finally, pipe-jacking dynamic and environmental interference experiments were conducted to verify the effectiveness of the CEEMDAN-LWT de-noising method. The de-noising effect of the proposed method was evaluated by SNR, RMSE, and Deviation and compared with the CEEMDAN and LWT de-noising methods. The results show that the CEEMDAN-LWT de-noising method has the best de-noising effect with good adaptivity and high accuracy. The navigation results of the pipe-jacking attitude before and after de-noising were compared and analyzed in the environmental interference experiment. The results show that the absolute error of the pipe-jacking pitch, roll, and heading angles is reduced by 39.86%, 59.45%, and 14.29% after de-noising. The maximum relative error of the pitch angle is improved from -0.74% to -0.44%, the roll angle is improved from 2.07% to 0.79%, and the heading angle is improved from -0.07% to -0.06%. Therefore, the CEEMDAN-LWT method can effectively suppress the random errors of the FOG signal caused by the environment and improve the measurement accuracy of the pipe-jacking attitude.

EFFECT OF WAVELET DE-NOISING ON THE CLASSIFICATION OF PIG BEHAVIOUR

To efficiently eliminate the noise generated by the triaxial accelerometer when collecting pigs’ behavioural data, this paper adopted SNR and MSE as the indexes to evaluate the de-noising effect of pigs’ acceleration signal under various combinations of wavelet basis, decomposition layer, threshold rule and threshold function. Based on the optimal wavelet parameter combinations, the de-noised data were divided into a training dataset and test dataset to conduct a 3-fold cross validation. The results showed that Db4 wavelet can achieve a satisfactory de-noising effect when used as a wavelet basis for 8 layers wavelet decomposition based on Rigrsure threshold rules and the new improved threshold function. As a result, compared with traditional wavelet hard threshold de-noising, soft threshold de-noising and EMD de-noising method, the improved threshold function improved the stability of signal filtering, which was shown to be more practical, effective and feasible. As such, wavelet de-noising was found to significantly improve the classification accuracy of all four behaviour classes (lying, standing, walking and exploring) considered for this study, and the overall major mean accuracy was improved from 0.680 to 0.826.

Improved Wavelet Threshold for Image De-noising.

With the development of communication technology and network technology, as well as the rising popularity of digital electronic products, an image has become an important carrier of access to outside information. However, images are vulnerable to noise interference during collection, transmission and storage, thereby decreasing image quality. Therefore, image noise reduction processing is necessary to obtain higher-quality images. For the characteristics of its multi-analysis, relativity removal, low entropy, and flexible bases, the wavelet transform has become a powerful tool in the field of image de-noising. The wavelet transform in application mathematics has a rapid development. De-noising methods based on wavelet transform is proposed and achieved with good results, but shortcomings still remain. Traditional threshold functions have some deficiencies in image de-noising. A hard threshold function is discontinuous, whereas a soft threshold function causes constant deviation. To address these shortcomings, a method for removing image noise is proposed in this paper. First, the method decomposes the noise image to determine the wavelet coefficients. Second, the wavelet coefficient is applied on the high-frequency part of the threshold processing by using the improved threshold function. Finally, the de-noised images are obtained to rebuild the images in accordance with the estimation in the wavelet-based conditions. Experiment results show that this method, discussed in this paper, is better than traditional hard threshold de-noising and soft threshold de-noising methods, in terms of objective effects and subjective visual effects.

An Image Denoising Method Based on Improved Wavelet Thresholding

This paper proposes an improved-threshold function aimed to enhance the de-noising performance of wavelet thresholding method. Firstly, the theory of wavelet transforms and characteristic of soft-threshold function and hard-threshold function was introduced. Then, an improved-threshold function was proposed. The new method overcomes the discontinuous in hard threshold de-noising method and reduces the permanent bias in soft threshold de-noising method. Last, the improved-threshold algorithm, soft-threshold algorithm, hard-threshold algorithm, disperse wavelet transform (DWT) and wiener filtering are used to reduce the noise in the same image. The experiment result show that the improved-threshold algorithm can get a better denoising effect than the traditional soft and hard thresholding de-noising algorithms.

A novel comprehensive evaluation method of the draft tube pressure pulsation of Francis turbine based on EEMD and information entropy

Undesirable pressure pulsations will be induced by flow instabilities in the draft tube when the Francis turbine operates at off-design conditions, which have multiple effects on the steady operation, and the effects vary with the operating condition. Therefore, the establishment of a comprehensive state evaluation index of the draft tube pressure pulsation (DTPP) is of great practical significance. In this study, a comprehensive evaluation method of DTPP has been proposed based on Ensemble Empirical Mode Decomposition (EEMD) and information entropy. First, the frequency components of DTPP are separated by the EEMD method which is more suitable for the analysis of non-stationary pressure pulsation signal. Second, to eliminate the effects of noise, a targeted EEMD noise reduction method which is combined with autocorrelation analysis and wavelet soft-threshold de-noising method is designed for the DTPP signal. Then, index energy values of all frequency components are calculated and normalized, and the values of the signals’ characteristic entropy are obtained by using the normalized index energy vector as the input vector. Finally, characteristic entropy values of all pressure pulsation signals measured from the draft tube are integrated into an index, which is named as the comprehensive characteristic entropy of DTPP (E_DTPP). The state of DTPP is comprehensively evaluated by E_DTPP. This method was evaluated by the actual measuring data of a 200 MW hydroelectric generating unit. The case study indicates that this single index can be utilized to evaluate the actual state of DTPP, and pressure pulsations will have distinct influence on the operation stability when E_DTPP increases obviously. The efforts of this study provide a novel and useful method for the comprehensive state evaluation of DTPP, and the E_DTPP could be used as an index for the stability of Francis turbine.

Mechanical Fault Diagnosis of High Voltage Circuit Breakers Utilizing EWT-Improved Time Frequency Entropy and Optimal GRNN Classifier.

The mechanical fault diagnosis results of the high voltage circuit breakers (HVCBs) are mainly determined by the feature vector and classifier used. In order to obtain more remarkable characteristics of signals and a robust classifier which is suitable for small sample classification, in this paper, a new mechanical fault diagnosis method is proposed. Firstly, the vibration signals of HVCBs are collected by a designed acquisition system, and the noise of signals is eliminated by a soft threshold de-noising method. Secondly, the empirical wavelet transform (EWT) is adopted to decompose the signals into a series of physically meaningful modes, and then, the improved time-frequency entropy (ITFE) method is used to extract the characteristics of the vibration signals. Finally, a generalized regression neural network (GRNN) is used to identify four types of vibration signals of HVCBs, while the smoothing parameter of GRNN is optimized by a loop traversal method. The experimental results show that by using this optimal classifier for fault diagnosis, the proposed fault diagnosis method has the better generalization performance and the recognition rate of unknown samples is over 95%, and the signal features obtained by the ITFE method are more significant than those of the traditional TFE method.

Impulse interference processing for MT data based on a new adaptive wavelet threshold de-noising method

Wavelet de-noising method is often used in the processing of magnetotelluric (MT) signal, and the wavelet hard and soft threshold de-noising method are the most popular although there is much room for improvement in the threshold function selection and threshold determination. A new adaptive wavelet threshold de-noising method was proposed by selecting a new threshold function and presenting an adaptive method for obtaining optimal threshold based on the multi-resolution Stein unbiased risk estimation. New threshold function and an adaptive method to determine threshold were discussed, and the principle and implementation of the algorithm were given. The simulated signal and the measured MT data contaminated by impulse interference were analyzed, and the obtained results were compared with those of the conventional wavelet hard and soft threshold de-noising methods. The results show that the proposed method overcomes the defects of the traditional wavelet soft and hard threshold due to a new threshold function, and a new method to determine the threshold of each layer is applied and provides an adaptive method for filtering MT data in the wavelet domain that requires a minimum of human intervention. The presented de-noising method is very suitable for suppressing the impulse interference for MT data and can get higher signal-to-noise ratio than the traditional wavelet threshold de-noising methods. After de-noising, the accurate data is loaded for further impedance estimation and geological interpretation.

English

In the process of GNSS deformation monitoring, it is inevitable that the monitoring data are contaminated by noise. Effectively mitigating the impact of noise on the measurements and thus improving the quality of the deformation data is the objective of GNSS data processing. Wavelet analysis can analyse the signal according to different frequencies of the signal. Simulation data can be used to determine the best wavelet basis function and select the appropriate decomposition level. In this paper, an improved threshold de-noising method is proposed, based on an analysis of conventional hard threshold de-noising, soft threshold de-noising and compulsory de-noising methods. The improved method was examined through a simulation analysis and applied in an engineering case. The results show that it effectively removed the noise at high frequencies while retaining data details and mutation. The de-noising ability of the proposed technique was better than that of the conventional methods. Moreover, this method significantly improved the quality of the deformation data.

Method of Ultrasonic Signal De-Noising Based on Lifting Wavelet Improved Threshold

The article established the mathematical model of ultrasonic flaw echo signals. First, the basic theory of wavelet transform is introduced, the principle of the wavelet threshold de-noising method is analyzed; Then on the basis of soft and hard threshold function, the paper proposes a method based on lifting wavelet de-noising. And from two aspects of signal-to-noise ratio (SNR) and mean square error (MSE) the de-noising performance is analysed. The results show that the method improved the shortcomings of soft and hard threshold de-noising method, and got a better de-noising performance and higher signal-to-noise ratio. So in real-time signal de-noising aspect the lifting wavelet has a very good application prospect.

EMG Signal De-Noising Based on Wavelet Packet μ Rhythm Threshold Method

Surface Electromyographic (SEMG) signal is characterized by physiological noise contained,in order to eliminate inclusion noise. In wavelet packet analysis domain,after analysising the traditional soft-threshold and hard-threshold de-noising method of characteriscs,a new method which is μ rhythm threshold method is provided to improve threshold function. In Matlab7.0,the relevant procedures and simulation show that the method can not only solve the hard-threshold de-noising continuous problem,but also solve the detects before and after the threshold treatment of the soft-threshold wavelet coefficients constant deviation. Meanwhile,the application of the method in the wavelet analysis shows that wavelet packet μ rhythm threshold method de-noising significantly better than wavelet μ rhythm threshold method,and proves that the wavelet packet has remarkable capacity to de-noising.

GPS Dynamic Filter Algorithm Based on Lifting Wavelet Transformation

It is difficult to establish a precise mathematical model of dynamic filtering for vehicle GPS navigation with Kalman filtering. And the traditional wavelet transformation has some shortness in real-time processing. This paper proposes a GPS dynamic filter algorithm based on the lifting wavelet transformation (LWT). It first decomposes the vehicle GPS navigation signal with the LWT. Then, it detects, eliminates and corrects the signal's gross error at different LWT resolution levels with statistical 3srule and polynomial interpolation method. The signal's noise is de-noised at different LWT resolution levels with modulus square soft-threshold de-noising method. Finally, the algorithm realizes real-time dynamic filtering for the vehicle GPS navigation system through reconstructing the de-noised LWT coefficients. The simulation results show that the algorithm is more effective than the Kalman filter in positioning precision. Compared with the traditional wavelet transformation, the speed is doubled for dynamic filtering even though the proposed algorithm only has little advantages on the positioning accuracy. Therefore, the algorithm is available for vehicle GPS navigation system.

Wavelet Transform Applied on Vehicle Air Flow Meter (AFM) Signal De-Noising

In engine compartment, it is difficult to eliminate the effect of interfering signals on vehicle AFM signal by the traditional processing method. According to the characteristic of AFM signal, this paper decomposed the noise signal for 4 layers by selecting Daubechies (db5) wavelet in Matlab based on wavelet theory. After decomposing, and then employed the soft-threshold de-noising method to eliminate noise. At last this paper used the inverse wavelet transform to reconstruct signals for signal de-noising and rebuilding. The test results show that this method can eliminate the noises of AFM signal effectively.

Research on Pitch Extraction Algorithm of Noisy Speech

Pitch detection in noisy environment plays an important role in speech analyzing and recognition. In the light of the properties of Hilbert-Huang transform and the EMD soft-threshold de-noising method, an effective pitch detection method for noisy speech signal is proposed in this paper. Firstly, the EMD soft-threshold de-noising method is applied to realize the background noise reduction, secondly, using the Hilbert-Huang transform to detect the pitch period of the de-noising speech signal. The analysis proposed in this paper show that, compared with the conventional methods of the pitch detection of the noisy speech, especially for the low signal to noise ratio (SNR), this approach has a higher accuracy.

Discussion on the Wavelet Adjustment Factor Threshold Noise Reduction Technology Based on DSP

Because of discontinuity at threshold, hard threshold de-noising leads to the additional oscillation at threshold when reconstructing the signal, so that the smoothness of the de-noised signal becomes weak; Soft threshold de-noising method can guarantee the good continuity of the signal. However, for the existence of the fixed bias between the estimated threshold and actual threshold, there are also deviations between the reconstructed signal and the actual signal existing deviations too. In this work, by using the high performance DSP as a signal processing tool, we reduced the noise of actual measured vibration signal collected from headstock of CA6140 lathe. By comparing, the result is the same as the noise reduction simulation calculated from MATLAB, which demonstrates the noise reduction effect of wavelet adjustment factor threshold de-noising apparently.

Research of Terahertz Spectra of Terbutaline Sulfate Based on Wavelet De-Noising

Terahertz spectra of terbutaline sulfate in the range of 0.2 to 2.2 THz was obtained by THz time-domain spectroscopy. The discrete wavelet transform was applied to de-noising terahertz waveforms. The signal was decomposed into five layers by wavelet decomposition, and then the high-frequency noise signal was eliminated by wavelet reconstruction. Another try was through calculating the standard deviation of the noise signal by the 1-th level signals which got from wavelet decomposition, and then the soft threshold and hard threshold de-noising method was employed respectively. The robustness of these wavelet de-noising methods was testified in this paper, and the absorption and refraction spectra of terbutaline sulfate were got at last. The result of experiment indicts that wavelet can enhance the signal to noise ratio of system and this paper provides a new way for the detection of terbutaline sulfate.

The Changes of Electrical Signals in Corn at Different Temperatures

Electrical signals in plants play the role of biological messages. It is significant to make them understood. In order to acquire the basic characteristics of the electrical signal in corn, wavelet soft-threshold de-noising method was introduced to reduce the noise for the acquisition signals. The amplitudes of electrical signals in corn were μV level, and the frequencies were below 1Hz, large parts of which were lower than 0.5Hz. The amplitudes were large, and the distribution of power spectrum was stable when the environment temperature between 20°C and 35°C. The ratio of signal below 0.1Hz gained when the temperature was above 35°C, while the amplitude reduced obviously. It can be considered that the disappearance of the high frequency and the reducing of the amplitudes were the signs of cell vital activity subsiding. Thus, it is possible to achieve the prediction life status according to the amplitudes and the frequencies of electrical signals in plants.

A new morphology method for enhancing power quality monitoring system

By means of mathematical morphology (MM), power quality monitoring systems can detect disturbances very soon. However, the signal under investigation is often corrupted by noises, and the performance of the MM would be greatly degraded. This paper proposed a new fast approach to detection of transient disturbances in a noisy environment. In the proposed approach, the appropriate morphologic structure element, new proper combination of the erosion and the dilation morphologic operators can enhance the MM’s capability. Furthermore, the soft-threshold de-noising method based on the wavelet transform (WT) was used for reference. In this way, the abilities of the MM can hence be restored. This method possesses the following advantages: high calculation speed, easy implementation of hardware and better use value. Finally, the validity of the proposed method is verified by the results of the simulation and the actual field tests.

Influence of probe scale and analysis method on measured hydrodynamic properties of gas-fluidized beds

The multi-scale properties of gas-fluidized bed hydrodynamics are examined using three different sized optical probes in a two-dimensional fluidized bed of fluid cracking catalyst particles. It is shown that the probe scale determines the scale of structures reflected in the signals analyzed using Fourier and wavelet transformation methods. The conventional fast Fourier transform method failed to remove the noise inevitably present in experimental measurements, while a soft thresholding wavelet transform method was successful in minimizing the noise. The level of noise at superficial gas velocities between 2.5 and 6.2 cm/s is shown to be comparable, and formed a basis for setting the threshold values used in the soft threshold de-noising method. The probe scale, as well as the analysis method, influences the results, and thus the interpretation of experimental hydrodynamic data.